一类非凸D.C.约束优化问题的UV-分解理论

UV-Decomposition Theory for a class of D.C. constrained Optimization Problem

UV-分解理论是近年来解决非光滑凸函数的二阶近似的一种有效的方法,并应用于解决非光滑凸函数的最优化问题。主要应用UV-分解理论对于一类D.C.函数的约束优化问题进行研究,借助于近似次微分的概念,得到类似的UV-空间分解,以及空间分解下的相应U-Lagrange函数与其最优解集W(u)的相关性质和二阶近似的结果。

The UV-Decomposition theory has been an effective method to solve the second - order approximation of non - smooth convex function and optimization problem of nonsmooth convex function recently. In this paper, the UV-Decomposition theory is used to study a class of nonconvex D. C. constrained optimization problem. By the proximal subdifferential, we get some results of UV- decomposition the corresponding, U - lagrange function, optimal solution set W（u） and the second -order approximation.